Giacomo Monari

Modelling the Galactic disc: perturbed distribution functions in the presence of spiral arms

Starting from an axisymmetric equilibrium distribution function (DF) in action space, representing a Milky Way thin disc stellar population, we use the linearized Boltzmann equation to explicitly compute the response to a three-dimensional spiral potential in terms of the perturbed DF. This DF, valid away from the main resonances, allows us to investigate a snapshot of the velocity distribution at any given point in three-dimensional configuration space. Moreover, the first order moments of the DF give rise to non-zero radial and vertical bulk flows -- namely breathing modes -- qualitatively similar to those recently observed in the extended Solar neighbourhood. We show that these analytically predicted mean stellar motions are in agreement with the outcome of test-particle simulations. Moreover, we estimate for the first time the reduction factor for the vertical bulk motions of a stellar population compared to the case of a cold fluid. Such an explicit expression for the full perturbed DF of a thin disc stellar population in the presence of spiral arms will be helpful in order to dynamically interpret the detailed information on the Milky Way disc stellar kinematics that will be provided by upcoming large astrometric and spectroscopic surveys of the Galaxy.

The effects of bar–spiral coupling on stellar kinematics in the Galaxy

We investigate models of the Milky Way disc taking into account simultaneously the bar and a two-armed quasi-static spiral pattern. Away from major resonance overlaps, the mean stellar radial motions in the plane are essentially a linear superposition of the isolated effects of the bar and spirals. Thus, provided the bar is strong enough, even in the presence of spiral arms, these mean radial motions are predominantly affected by the Galactic bar for large scale velocity fluctuations. This is evident when comparing the peculiar line-of-sight velocity power spectrum of our coupled models with bar-only models. However, we show how forthcoming spectroscopic surveys could disentangle bar-only non-axisymmetric models of the Galaxy from models in which spiral arms have a significant amplitude. We also point out that overlaps of low-order resonances are sufficient to enhance stellar churning within the disc, even when the spirals amplitude is kept constant. Nevertheless, for churning to be truly non-local, stronger or (more likely) transient amplitudes would be needed: otherwise the disc is actually mostly unaffected by churning in the present models. Finally, regarding vertical breathing modes, the combined effect of the bar and spirals on vertical motions is a clear non-linear superposition of the isolated effects of both components, significantly superseding the linear superposition of modes produced by each perturber separately, thereby providing an additional effect to consider when analysing the observed breathing mode of the Galactic disc in the extended Solar neighbourhood.

Spiral and bar driven peculiar velocities in Milky Way sized galaxy simulations

We investigate the kinematic signatures induced by spiral and bar structure in a set of simulations of Milky Way-sized spiral disc galaxies. The set includes test particle simulations that follow a quasi-stationary density wave-like scenario with rigidly rotating spiral arms, and N-body simulations that host a bar and transient, co-rotating spiral arms. From a location similar to that of the Sun, we calculate the radial, tangential and line-of-sight peculiar velocity fields of a patch of the disc and quantify the fluctuations by computing the power spectrum from a two-dimensional Fourier transform. We find that the peculiar velocity power spectrum of the simulation with a bar and transient, co-rotating spiral arms fits very well to that of APOGEE red clump star data, while the quasi-stationary density wave spiral model without a bar does not. We determine that the power spectrum is sensitive to the number of spiral arms, spiral arm pitch angle and position with respect to the spiral arm. However, it is necessary to go beyond the line of sight velocity field in order to distinguish fully between the various spiral models with this method. We compute the power spectrum for different regions of the spiral discs, and discuss the application of this analysis technique to external galaxies.

The Galactic bar and the large scale velocity gradients in the Galactic disk

We investigate whether the cylindrical (galactocentric) radial velocity gradient of ∼− 3k m s −1 kpc −1 , directed radially from the Galactic center and recently observed in the stars of the solar neighborhood with the RAVE survey, can be explained by the resonant effects of the bar near the solar neighborhood. We compared the results of test particle simulations of the Milky Way with a potential that includes a rotating bar with observations from the RAVE survey. To this end we applied the RAVE selection function to the simulations and convolved these with the characteristic RAVE errors. We explored different “solar neighborhoods” in the simulations, as well as different bar models. We find that the bar induces a negative radial velocity gradient at every height from the Galactic plane, outside the outer Lindblad resonance and for angles from the long axis of the bar compatible with the current estimates. The selection function and errors do not wash away the gradient, but often make it steeper, especially near the Galactic plane, because this is where the RAVE survey is less radially extended. No gradient in the vertical velocity is present in our simulations, from which we may conclude that this cannot be induced by the bar.

Tracing the Hercules stream with Gaia and LAMOST: new evidence for a fast bar in the Milky Way

The length and pattern speed of the Milky Way bar are still controversial. Photometric and spectroscopic surveys of the inner Galaxy, as well as gas kinematics, favour a long and slowly rotating ba ...

Staying away from the bar: the local dynamical signature of slow and fast bars in the Milky Way

Both the three-dimensional density of red clump giants and the gas kinematics in the inner Galaxy indicate that the pattern speed of the Galactic bar could be much lower than previously estimated. Here, we show that such slow bar models are unable to reproduce the bimodality observed in local stellar velocity space. We do so by computing the response of stars in the Solar neighbourhood to the gravitational potential of slow and fast bars, in terms of their perturbed distribution function in action-angle space up to second order, as well as by identifying resonantly trapped orbits. We also check that the bimodality is unlikely to be produced through perturbations from spiral arms, and conclude that, contrary to gas kinematics, local stellar kinematics still favour a fast bar in the Milky Way, with a pattern speed of the order of almost twice (and no less than 1.8 times) the circular frequency at the Suns position. This leaves open the question of the nature of the long flat extension of the bar in the Milky Way.

THE IMPRINTS OF THE GALACTIC BAR ON THE THICK DISK WITH RAVE

We study the kinematics of a local sample of stars, located within a cylinder of radius centered on the Sun, in the RAVE data set. We find clear asymmetries in the - velocity distributions of thin and thick disk stars: there are more stars moving radially outward for low azimuthal velocities and more radially inward for high azimuthal velocities. Such asymmetries have been previously reported for the thin disk as being due to the Galactic bar, but this is the first time that the same type of structures are seen in the thick disk. Our findings imply that the velocities of thick-disk stars should no longer be described by Schwarzschild’s, multivariate Gaussian or purely axisymmetric distributions. Furthermore, the nature of previously reported substructures in the thick disk needs to be revisited as these could be associated with dynamical resonances rather than to accretion events. It is clear that dynamical models of the Galaxy must fit the 3D velocity distributions of the disks, rather than the projected 1D, if we are to understand the Galaxy fully.

Distribution functions for resonantly trapped orbits in the Galactic disc

The present-day response of a Galactic disc stellar population to a non-axisymmetric perturbation of the potential has previously been computed through perturbation theory within the phase-space coordinates of the unperturbed axisymmetric system. Such an Eulerian linearized treatment, however, leads to singularities at resonances, which prevent quantitative comparisons with data. Here, we manage to capture the behaviour of the distribution function (DF) at a resonance in a Lagrangian approach, by averaging the Hamiltonian over fast angle variables and re-expressing the DF in terms of a new set of canonical actions and angles variables valid in the resonant region. We then follow the prescription of Binney, assigning to the resonant DF the time average along the orbits of the axisymmetric DF expressed in the new set of actions and angles. This boils down to phase-mixing the DF in terms of the new angles, such that the DF for trapped orbits depends only on the new set of actions. This opens the way to quantitatively fitting the effects of the bar and spirals to Gaia data in terms of DFs in action space.

The escape speed curve of the Galaxy obtained from Gaia DR2 implies a heavy Milky Way

We measure the escape speed curve of the Milky Way based on the analysis of the velocity distribution of

Correlations between age, kinematics, and chemistry as seen by the RAVE survey

\sim 2850